I visited Qsar Amra on a half-day trip from Madaba with a rental car. It is located about an hour east of Amman, and well sign-posted from the main road.
At first, this desert castle seems a bit disapointing. The outside walls were been restored and surrounded by scafoldings.
The real treasure lies within. The walls are painted (some of them are also being renovated). It shows very fine figurative murals depicting humans in pleasure activities (hunting, bathing) princes and angels, animals of all kinds, even a bear playing a music instrument.
One would not expect this kind of painting from the 8th century Umayyads dinasty.
They is a small museum near the car park, giving explanation on the paintings and the buildings (in fact a hunting and pleasure palace rather than a real desert castle).
There was not entrance fee. And we were the only tourists on the site.